Global Existence Of Solutions To 1D Compressible Navier-Stokes System With Outer Pressure In The Half-Space

The compressible Navier-Stokes(N-S)equation describes the motion of viscous compressible fluid,which is the theoretical basis of fluid dynamics and a very important mathematical model in fluid dynamics.The equation has a wide range of applications in aerodynamics,marine science,materials science,aerospace,petrochemical,semiconductor physics and many other fields.The existence,uniqueness and large time behavior of its solution have attracted many scholars at home and abroad.This paper mainly studies the global existence of strong solutions to the external pressure problem of one-dimensional half-space compressible N-S system.At present,there are abundant research results on the initial boundary value problem of one-dimensional compressible N-S equations without vacuum.However,there are few studies on the half-space region,especially the external pressure boundary.This paper proves the global existence of strong solutions,and enriches and improves the theoretical system of compressible N-S equations.Firstly,this paper mainly introduces the research background,main research progress and research contents of compressible N-S systems,and then introduces some space definitions,inequalities and theorems related to this paper.Secondly,this paper overcomes the difficulties caused by half-space and boundary terms,and proves the upper and lower bounds of specific volume and temperature independent of time and the priori estimates independent of time.Among them,after obtaining a new estimate,this paper obtains the L∞(0,∞;L2(Ω))-norm estimation of vx.After that,this paper extends the local solutions to the global,thus obtaining the global existence of the strong solutions.Finally,this paper summarizes the proof of the main theorem and puts forward the subject that can be further studied in the future.